Ex 9.4, 1 - Find general solution: dy/dx = 1 - cos x/1+cosx - Variable separation - Equation given

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  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise
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Ex 9.4, 1 For each of the differential equations in Exercises 1 to 10, find the general solution : 𝑑𝑦﷮𝑑𝑥﷯= 1 − cos﷮𝑥﷯﷮1+ cos﷮𝑥﷯﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 1 − cos﷮𝑥﷯﷮1 + cos﷮𝑥﷯﷯ dy = 1 − cos﷮𝑥﷯﷮1 + cos﷮𝑥﷯﷯ dx. Putting values in equation dy = 2 sin﷮2﷯ ﷮ 𝑥﷮2﷯﷯ ﷮2 cos﷮2﷯ ﷮ 𝑥﷮2﷯﷯﷯ dx dy = sin﷮2﷯ ﷮ 𝑥﷮2﷯﷯ ﷮ cos﷮2 ﷯﷮ 𝑥﷮2﷯﷯﷯ dx dy = tan2 𝑥﷮2﷯ dx Putting tan2 𝑥﷮2﷯ = sec2 𝑥﷮2﷯ − 1 dy = sec2 𝑥﷮2﷯ − 1﷯𝑑𝑥 Integrating both sides ﷮﷮𝑑𝑦﷯ = ﷮﷮ 𝑠𝑒𝑐2 𝑥﷮2﷯−1﷯﷯dx y = ﷮﷮𝑠𝑒𝑐2 𝑥﷮2﷯𝑑𝑥− ﷮﷮𝑑𝑥﷯﷯ y = 1﷮ 1﷮2﷯﷯ tan 𝑥﷮2﷯ − x + C y = 2 tan 𝑥﷮2﷯ − x + c y = 2 tan 𝑥﷮2﷯ − x + C y = 𝟐 tan 𝒙﷮𝟐﷯ − x + C is the general solution

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